Evaluate the integral without using tables. \int_{0}^{1}\frac{dx}{\sqrt{1-x^{2}}}

BenoguigoliB 2021-11-08 Answered
Evaluate the integral without using tables.
01dx1x2
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Expert Answer

yagombyeR
Answered 2021-11-09 Author has 92 answers
Step 1
Given,
I=01dx1x2
Step 2
Formula used:
dx1x2=sin1(x)+C
xndx=xn+1n+1+C
Step 3
Apply the above formula, we get
I=01dx1x2
=[sin1(x)]01
=sin1(1)sin1(0)
=sin1(sin(π2))sin1(sin(0))
=π20
=π2
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